Answer:
58
Step-by-step explanation:
We are given the arithmetic sequence:-
-12,-7,-2,3,...
First, find the common difference which we can obtain by:-
[tex] \displaystyle \large{d = a_{n + 1} - a_n}[/tex]
Check:-
-7-(-12) = -7+12 = 5
-2+7 = 5
3+2 = 5
Therefore, our common difference is 5.
General Arithmetic Term
[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]
Since we want to find the 15th term, substitute a1 = -12, n = 15 and d = 5.
[tex] \displaystyle \large{a_{15}= - 12 + (15 - 1)5} \\ \displaystyle \large{a_{15}= - 12 + (14)5} \\ \displaystyle \large{a_{15}= - 12 + 70} \\ \displaystyle \large{a_{15}= 58} \\ [/tex]
